Seminar 23 Mars

This week’s seminar will be given by Florian List and will take place at 1pm on Thursday, as usual.

Title: Iterative methods for solving Richards’ equation

Abstract: This presentation concerns linearization methods for efficiently solving the Richards’ equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards’ equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards’ equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L-scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The proof of the convergence of the L-scheme is presented and the convergence of the other methods is discussed. A new scheme is proposed, the L-scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples.